CKMfitter

Preliminary results as of BEAUTY 09

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The global CKM fit: Inputs and Numerical results

The global CKM fit in the large (ρ-bar,η-bar) plane

The global CKM fit in the small (ρ-bar,η-bar) plane (zoom)

Constraint from BR(B⁺→τ⁺ ν)

Constraint from decays B→ V γ

Constraints on the angle α/ϕ₂ from charmless B decays

Constraints on the angle γ/ϕ₃ from B decays to charm

Constraints on |sin(2β+γ)|

New Physics in Mixing

Numerical results:

The results of the global CKM analysis include:

Wolfenstein parameters,
UT angles and sides,
UT_sangle and apex,
CKM elements,
theory parameters,
rare branching fractions (B->lν, B->ll).

Numerical Results

The global CKM fit in the large (ρ-bar,η-bar) plane:

Constraints in the (ρ-bar,η-bar) plane. The |Vub| constraint has been splitted in the two contributions: |Vub| from inclusive and exclusive semileptonic decays (plain dark green) and |Vub| from B⁺→τ⁺ ν (hashed green). The red hashed region of the global combination corresponds to 68% CL.

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Constraints in the (ρ-bar,η-bar) plane. The red hashed region of the global combination corresponds to 68% CL.

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The global CKM fit in the small (ρ-bar,η-bar) plane (zoom):

Zoomed constraints in the (ρ-bar,η-bar) plane. The |Vub| constraint has been splitted in the two contributions: |Vub| from inclusive and exclusive semileptonic decays (plain dark green) and |Vub| from B⁺→τ⁺ ν (hashed green). The red hashed region of the global combination corresponds to 68% CL.

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Zoomed constraints in the (ρ-bar,η-bar) plane. The red hashed region of the global combination corresponds to 68% CL.

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Zoomed constraints in the (ρ-bar,η-bar) plane not including the angle measurements in the global fit.

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Zoomed constraints in the (ρ-bar,η-bar) plane including only the angle measurements in the global fit.

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Zoomed constraints in the (ρ-bar,η-bar) plane including the CP conserving quantities in the global fit, i.e., |V_ub| (semileptonic and B⁺→τ⁺ ν), Δm_d, Δm_d & Δm_s.

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Zoomed constraints in the (ρ-bar,η-bar) plane including the CP violating quantities in the global fit, i.e., sin(2β), α, γ and ε_K.

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Zoomed constraints from "Tree" quantities in the (ρ-bar,η-bar) plane (γ(DK) and α from the isospin analysis with the help of sin2β (charmonium), which gives another tree only γ measurement (the only assumption is that the ΔI=3/2 b-->d EW penguin amplitude is negligible)).

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Zoomed constraints from "Loop" quantities in the (ρ-bar,η-bar) plane.

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Zoomed constraints in the (ρ-bar,η-bar) plane not including the braching ratio of B⁺ → τ⁺ν in the global fit.

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Zoomed constraints in the (ρ-bar,η-bar) plane not including the measurement of sin2β in the global fit.

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Constraint from the B⁺→τ⁺ ν branching ratio:

There is a discrepancy in the CKM global fit, because of the world average for sin2β and the world average for BR(B→τν).

There is a specific correlation between the two quantities in the global fit that is a bit at odds with the direct experimental determination. This is best viewed in the (sin2β,BR(B→τν)) plane, regarding the prediction from the global fit without using these measurements. The cross corresponds to the experimental values with 1 sigma uncertainties.

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The shape of the correlation can be understood by considering the ratio BR(B→τν)/Δm_d, where the decay constant f_{B_d} cancels, leaving limited theoretical uncertainties (the ratio depends only on the bag parameter B_{B_d}). Thus from the observables BR(B→τν) and Δm_d one gets an interesting constraint in the (ρbar,ηbar) plane, which does not match perfectly with the global fit output.

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To have a closer look, one can write the full formula for the ratio

where one explicitly sees that the correlation between BR(B→τν) and the angle β is controlled by the values of B_{B_d}, and the angles α and γ. This can be checked explicitly by comparing the above analytical formula with the colored region in the (sin2β,BR(B→τν)) plane. In other words the discrepancy is not driven by the value of semileptonic |V_ub|, nor by the decay constant f_{B_d}.

To quantify the discrepancy one can compare the indirect fit prediction for BR(B→τν) with the measurement. The deviation here is 2.4 sigmas.

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A simpler test is the comparison of the prediction of B_{B_d} from the above analytical formula (having only BR(B→τν), Δm_d, α, β, γ and |V_ud| as inputs, that is an almost completely theory-free determination of B_{B_d}) with the current lattice determination B_{B_d} = 1.18 ± 0.14. For this test the deviation is 2.6 sigmas, dominated by the error on BR(B→τν), α, γ and B_{B_d}.

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From the above branching ratio one can derive a value for f_{B_d} (288⁺³⁴_-32 MeV) as well and compare it with respect to our Lattice QCD average (190.6 ± 20.6 MeV).

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Finally one can compare the contributions to the global fit and our Lattice averages on the quantities f_{B_d} vs.f_{B_d} Sqrt(B_{B_d}).

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Constraint from decays B →V γ:

No update

See Summer 08 results (here)

Constraints on the angle α/ϕ₂ from charmless B decays:

No update

See Moriond 09 results (here)

Constraints on the angle γ/ϕ₃ from B decays to charm:

Constraints on γ/ϕ₃ from world average D(*)K(*) decays (GLW+ADS) and Dalitz analyses (GGSZ) compared to the prediction from the global CKM fit (not including these measurements): γ[combined] = (73⁺²²_-25)°

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Constraint on the ratio of interfering amplitudes r_B of the decay B → DK from world average D(*)K(*) decays (GLW+ADS) and Dalitz analyses (GGSZ): r_B(DK) = 0.096^+0.019_-0.016.

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Constraint on the ratio of interfering amplitudes r_B of the decay B → DK from world average D(*)K(*) decays (GLW+ADS) and Dalitz analyses (GGSZ): r_B(DK) = 0.129 ^+0.025_-0.027.

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Constraint on the ratio of amplitudes r_B of the decay B → DK^*: r_B(DK^*)= 0.163^+0.075_-0.105.

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Constraint on the strong phase between the interfering amplitudes of the decay B → DK from world average D(*)K(*) decays (GLW+ADS) and Dalitz analyses (GGSZ): δ_B(DK) = 114⁺²⁰_-24)°.

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Constraint on the strong phase between the interfering amplitudes of the decay B → D^*K: δ_B(D^*K) = (-34⁺¹⁶_-19)°.

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Constraint on the strong phase between the interfering amplitudes of the decay B → DK^*: δ_B(DK^*) = (43⁺¹⁰⁴_-25)°.

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Constraints on |sin(2β+γ)|:

Constraints on |sin(2β+γ)| from the measurement of time-dependent CP asymmetries in D(*)π (ρ); Summer 08 HFAG average including a preliminary Belle ICHEP08 update for D*π is used as input. The extraction of the UT-angle combination relies on SU(3) symmetry for the estimates of the suppressed-to-leading amplitude ratios. We use for r^(*) the values of BABAR Collaboration, arXiv:0803.4296 [hep-ex] (aka Phys.Rev.D78:032005,2008) with an updated average for the ratio fDs/fD equal to 1.163 ± 0.007 (using recent inputs from ETMC08, FNAL-MILC07, and HPQCD07 Lattice groups) and treat the SU(3) uncertainty by using the method described in Max Baak's talk presented at CKM06 workshop (here)

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Translation of this result into γ (using sin(2β) as additional input and choosing among the four solutions to the SM one). γ[GLW+ADS+GGSZ+|sin(2β+γ)|] = (75 ⁺¹⁶_-19)°.

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Constraints from |sin(2β+γ)| in the (ρ-bar,η-bar) plane.

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Constraints on New physics in B_d,s-Meson Mixing:

No update

See Moriond 09 results (here)